Self-trapping polaron

Such renormalization can be obtained in the framework of the small polaron theory [3]. Scoq is the energy gain of exciton localization. Let us note that the condition (20) and, therefore, Eq.(26) is correct for S 5/wo and arbitrary B/ujq for the lowest energy of the exciton polaron. So Eq.(26) can be used to evaluate the energy of a self-trapped exciton when the energy of the vibrational or lattice relaxation is much larger then the exciton bandwidth. 

It has been shown theoretically that an extra electron or hole added to a one-dimensional (ID) system will always self-trap to become a large polaron [31]. In a simple ID system the spatial extent of the polaron depends only on the intersite transfer integral and the electron-lattice coupling. In a 3D system an excess charge carrier either self-traps to form a severely locahzed small polaron or is not localized at all [31]. In the literature, as in the previous sections, it is frequently assumed for convenience that the wavefunction of an excess carrier in DNA is confined to one side of the duplex. This is, of course, not the case, although it is likely, for example, that the wavefunction of a hole is much larger on G than on the complementary C. In any case, an isolated DNA molecule is truly ID and theory predicts that an excess electron or hole should be in a polaron state. 

The energy E will necessarily have this minimum, but its value at this point can be positive or negative only in the latter case will a stable self-trapped particle (i.e. a small polaron) form. This is most likely to occur for large effective mass, and thus for holes in a narrow valence band or for carriers in d-bands. If the polaron is unstable then there is practically no change in the effective mass of an electron or hole in equilibrium in the conduction or valence band. 

Another mechanism that has been proposed is that the carriers move as small polarons20. A small polaron is a carrier that is self trapped in a well created by the lattice distortion. This lattice distortion is formed when a carrier stays sufficiently long in a position to polarize the medium around it. The applied field can lower the polaron barrier in a PF fashion and increase the mobility. The polaron transport model is attractive in that the mobilities in this mechanism are not critically dependent on the sample preparation. 

An electron or a hole injected on such a chain cannot then be present as a charged soliton. However, here again the electron-phonon interaction is important. If a charge is put on a true one-dimensional system, it always becomes dressed by a lattice distortion that is, it will self-trap and form a polaron [68], an extension that depends on the ratio of the electron-phonon coupling to the electronic intersite coupling t. Presumably, the time needed to relax the one-dimensional lattice around the charge is very short, on the order of one vibrational period or 100 fs. 

In this case, the overall energy of the polaron is negative and the electron will be self-trapped. If a is equal to the lattice constant, the polaron is called a small... 

We have pinpointed the essential processes contributing to the slow component in the time-dependent absorption signal as orientational relaxation of the liquid during electron solvation. But what other evidence is there to describe the fast, unresolved but significant IR absorption that is ascribed to localization To what extent does the local liquid structure and density continue to play a quantitative role at earlier times Is the electron self-trapped, as in a polaron model, during localization It is to these... 

The ideas just reviewed are used below to discuss the electronic structure of specific azides. Such features of the band structure as the magnitudes of the effective masses and the positions of the band extrema in momentum space are - not sufficiently understood to warrant discussion. It should also be noted that electrons and holes tend to polarize the medium in which they move. If they are not particularly mobile, ionic nuclei have time to adjust to their presence by moving toward or away from them. An electron or hole is then dressed by this polarization and either carries it about (as an electron or hole polaron) or is trapped by it (self-trapping). Young [64] suggested that exciton models in the alkali azides should take the polaron character of electrons and holes into account. No one has yet attempted such a description. While it may be that polaron effects are necessary for a proper understanding of electronic structure, the discussion here is limited to a model involving undressed holes and electrons. 

An additional complication arises from the fact that the probability of an electron (or hole) being self-trapped due to the electron - phonon interaction increases strongly as the electronic wave function shrinks in size to the order of atomic dimensions (Emin, 1982). A consequence of this is that electrons in disorder-induced localized states are believed to be more susceptible to small polaron formation and self-trapping than are ordinary extended-state electrons (Emin, 1984 Cohen et al, 1983). Thus, not only does the disordered structure of amorphous semiconductors introduce new physical phenomena, namely, the mobility edge, but also the effect of known phenomena, such as the electron - phonon interaction, can be qualitatively different. 

One can imagine influences of the muon also on B. Firstly, the muon distorts the lattice aroimd its position (self-trapping, small polaron). This can change the dipolar sum over the first neighbor shell. Secondly, the muon may not be that well localized at r = 0, even if it does not diffuse from site to site. The muon could have an extended wave... 

The small polaron theories for hydrogen tunnelling in metals assume that the asymmetry A is mostly caused by the H self-trapping energy, which has to be thermally overcome by a dynamic tilting of the potential before instantaneous tunnelling can occur in the coincidence configuration... 

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